Packing Nonspherical Particles - Princeton University

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Definitions A periodic packing is obtained by placing a fixed nonoverlapping configuration of N particles in each fundamental cell. Thus, the density is φ = Nv1 Vol(F) . A particle is centrally symmetric if it has a center C that bisects every chord through C connecting any two boundary points. centrally symmetric centrally symmetric non-centrally symmetric 2 equivalent ⊥ axes 2 inequivalent ⊥ axes . – p. 6/28
Hyperuniformity for General Point Patterns Torquato and Stillinger, PRE (2003) R Ω R Ω Denote by σ 2 (R) ≡ 〈N 2 (R)〉 − 〈N(R)〉 2 the number variance. For a Poisson point pattern and many correlated point patterns, σ 2 (R) ∼ R d . We call point patterns whose variance grows more slowly than R d hyperuniform (infinite-wavelength fluctuation vanish). This implies that structure factor S(k) → 0 for k → 0. The hyperuniformity concept enables us to classify crystals and quasicrystals together with special disordered point processes. All crystals and quasicrystals are hyperuniform such that σ 2 (R) ∼ R d−1 – number variance grows like window surface area. Many different MRJ particle packings are hyperuniform with S(k) ∼ k for k → 0. Donev, Stillinger & Torquato, 2005; Berthier et al., 2011; Zachary, Jiao & Torquato, 2011; Kurita and Weeks, 2011. . – p. 7/28
Page 1 and 2: Packing Nonspherical Particles: All
Page 3 and 4: Geometric Structure Approach to Jam
Page 5 and 6: 3D Hard Spheres in Equilibrium Torq
Page 7 and 8: Dense Packings of Nonspherical Part
Page 9: Definitions A periodic packing is o
Page 13 and 14: Packings of the Platonic and Archim
Page 15 and 16: Adaptive Shrinking Cell Optimizatio
Page 17 and 18: Kepler-Like Conjecture for a Class
Page 19 and 20: Superballs A d-dimensional superbal
Page 21 and 22: Conjecture 2: Another Organizing Pr
Page 23 and 24: Packings of Truncated Tetrahedra Th
Page 25 and 26: Maximally Dense Ellipsoidal Packing
Page 27 and 28: Generalizations of the Organizing P
Page 29 and 30: φ J 0.74 0.72 0.7 0.68 0.66 0.64 Z
Page 31 and 32: MRJ Packings of Nontiling Platonic
Page 33 and 34: Generalization of Hyperuniformity t

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